How to find the count of particular object in array using javascript?

i have an array of objects like below,

const arr_obj = [
    {
        id: '1',
        children: [],
        type: 'TYPE1',
    },
    {
         id: '2',
         children: [
             {
                  id: '1',
                  children: [
                      {
                          //some attributes
                       }
                  ],
                  type: 'MAIN',
             },
             {
                  id: '2',
                  children: [
                      {
                          //some attributes
                       }
                  ],
                  type: 'MAIN',
             },
             {
                  id: '3',
                  children: [
                      {
                          //some attributes
                       }
                  ],
                  type: 'MAIN',
             },
         ]
         type: 'TYPE2',
     },
     {
         id: '3',
         children: [
             {
                  id: '4',
                  children: [
                      {
                          //some attributes
                       }
                  ],
                  type: 'MAIN',
             },
             {
                  id: '5',
                  children: [
                      {
                          //some attributes
                       }
                  ],
                  type: 'MAIN',
             },
             {
                  id: '6',
                  children: [
                      {
                          //some attributes
                       }
                  ],
                  type: 'MAIN',
             },
         ]
         type: 'TYPE2',
     }
 ]

Now i have to find out the count of type: ‘MAIN’. these ‘MAIN’ will be within type: “type2”

so the expected count is 6. the outer children array can be empty and sometimes inner children array with type: “type2” is not there at all examples like below,

children: [] //empty array


children: [
    {
        id: '1',
        children: [],
        type: 'TYPE1',
    },
] //no children with type: 'TYPE2'

could someone help me with this. i am new to programming. thanks.